{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:20:43Z","timestamp":1758824443357},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2012,2,2]],"date-time":"2012-02-02T00:00:00Z","timestamp":1328140800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2012,3]]},"abstract":"Let k<\/jats:italic> and \u2113 be positive integers. With a graph G<\/jats:italic>, we associate the quantity c<\/jats:italic>k<\/jats:italic>,\u2113<\/jats:sub>(G<\/jats:italic>), the number of k<\/jats:italic>-colourings of the edge set of G<\/jats:italic> with no monochromatic matching of size \u2113. Consider the function c<\/jats:italic>k<\/jats:italic>,\u2113<\/jats:sub>: <\/jats:private-char> given by c<\/jats:italic>k<\/jats:italic>,\u2113<\/jats:sub>(n<\/jats:italic>) = max {c<\/jats:italic>k<\/jats:italic>,\u2113<\/jats:sub>(G<\/jats:italic>): |V<\/jats:italic>(G<\/jats:italic>)| = n<\/jats:italic>}, the maximum of c<\/jats:italic>k<\/jats:italic>,\u2113<\/jats:sub>(G<\/jats:italic>) over all graphs G<\/jats:italic> on n<\/jats:italic> vertices. In this paper, we determine c<\/jats:italic>k<\/jats:italic>,\u2113<\/jats:sub>(n<\/jats:italic>) and the corresponding extremal graphs for all large n<\/jats:italic> and all fixed values of k<\/jats:italic> and \u2113.<\/jats:p>","DOI":"10.1017\/s0963548311000484","type":"journal-article","created":{"date-parts":[[2012,3,19]],"date-time":"2012-03-19T15:20:59Z","timestamp":1332170459000},"page":"203-218","source":"Crossref","is-referenced-by-count":12,"title":["Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size"],"prefix":"10.1017","volume":"21","author":[{"given":"CARLOS","family":"HOPPEN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YOSHIHARU","family":"KOHAYAKAWA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HANNO","family":"LEFMANN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,2,2]]},"reference":[{"key":"S0963548311000484_ref10","doi-asserted-by":"publisher","DOI":"10.4310\/JOC.2010.v1.n4.a4"},{"key":"S0963548311000484_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548309009948"},{"key":"S0963548311000484_ref13","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199604)21:4<441::AID-JGT10>3.0.CO;2-I"},{"key":"S0963548311000484_ref7","doi-asserted-by":"crossref","unstructured":"[7] Hoppen C. , Kohayakawa Y. and Lefmann H. Edge colorings of graphs avoiding some fixed monochromatic subgraph with linear Tur\u00e1n number. Electron. Notes Discrete Math. (Proc. EUROCOMB 2011), in press doi:10.1016\/j.endm.2011.09.076.","DOI":"10.1016\/j.endm.2011.09.076"},{"key":"S0963548311000484_ref11","unstructured":"[11] Pikhurko O. and Yilma Z. B. The maximum number of K 3-free and K 4-free edge 4-colorings. J. London Math. Soc., to appear."},{"key":"S0963548311000484_ref6","doi-asserted-by":"crossref","unstructured":"[6] Lefmann H. , Hoppen C. and Kohayakawa Y. (2011) Hypergraphs with many Kneser colorings. Europ. J. of Combin., doi:10.1016\/j.ejc.2011.09.025 (in press).","DOI":"10.1016\/j.ejc.2011.09.025"},{"key":"S0963548311000484_ref12","first-page":"399","volume-title":"Probl\u00e8mes Combinatoires et Th\u00e9orie des Graphes: Colloq. Internat. CNRS, Orsay 1976","author":"Szemer\u00e9di","year":"1978"},{"key":"S0963548311000484_ref8","unstructured":"[8] Lefmann H. and Person Y. Exact results on the number of restricted edge colorings for some families of linear hypergraphs. Submitted."},{"key":"S0963548311000484_ref1","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610704005563"},{"key":"S0963548311000484_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2004.12.004"},{"key":"S0963548311000484_ref5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1946-08715-7"},{"key":"S0963548311000484_ref3","first-page":"39","article-title":"Some new applications of probability methods to combinatorial analysis and graph theory. In","volume":"X","author":"Erd\u0151s","year":"1974","journal-title":"Proc. Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing, Boca Raton 1974, Congressus Numerantium"},{"key":"S0963548311000484_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000484","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T01:25:43Z","timestamp":1556241943000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000484\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,2]]},"references-count":13,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,3]]}},"alternative-id":["S0963548311000484"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000484","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,2]]}}}